Ordinarily, in order to obtain a nominal image of a scene and also a zoomed image of the scene, a distance s between the imaging sensor and a lens of the optical system and a focal length f of the optical system have to be increased. This is evident, for example, from the thin lens magnification formulae |M|=s/S and |M|=f/S (for S>>f); here, M is the magnification of the optical system and its absolute value needs to be increased for optical zooming and S is a distance between the lens and the scene. The zoomed image contains a smaller field of view of the scene. The field of view is reduced during the optical zooming.
In FIG. 1 there is schematically shown an exemplary optical zooming arrangement 10 including three lenses L1-L3, lens L2 of which changes its position and therefore changes the effective focal length of the whole arrangement. While an object plane PO is to the left of the arrangement and an image plane PI is to the right of the arrangement, a shift of lens L2 from the left to the right causes zooming out and a reverse movement causes zooming in. Therefore, imaging the same scene S with zooming arrangement 10 having lens L2 in positions P1, P2 and P3 results in images I1, I2 and I3 of three different sizes. When these images are captured with a CMOS array, image I1 takes its largest portion and image I3 takes its smallest portion. In arrangement 10 zooming does not require lens flexing. Arrangement 10 is relatively heavy, occupies a relatively large volume, and it is of a relatively low robustness.
Generally, zooming is desired if it can provide a higher resolution. The resolution is typically limited by the worst of the diffraction-limited resolution of the optical system and the geometrical resolution of the imaging sensor. The diffraction limit is commonly defined as a minimum diameter d of spot of light formed at the focus of a lens:d=1.22λf/a  (B1)where λ is the wavelength of the light and a is the diameter of the lens. In other words, the diffraction limited spot is a width of a Point Spread Function (PSF). The geometrical limit is defined by a size of a photodetector pixel or by a size of a film grain.
Imaging systems, such as those capable of zooming, are frequently configured in such a way, that their smallest diffractive-limited spot exceeds or equals the geometrical resolution: this allows avoiding the effect known as aliasing. The aliasing is associated with the following: if an object scene (or its region) has a relatively energetic spatial harmonic with a spatial frequency greater than the Nyquist frequency of the imaging sensor, then capturing of this object scene is accompanied by undersampling of this harmonic. The harmonic is captured as it has a different (lower), “alias”, spatial frequency. This leads to the appearance of a distortion of the object scene (or of its region) captured in the image. The aliasing effect is thus typically considered as a problem in imaging.
A typical imaging system is thus diffraction-limited: then it contains no aliasing, independently on the object scene. In fact, the optical system of the diffraction-limited imaging system filters out high-frequency content. Particularly, in case of coherent light imaging the optical system's Coherent Transfer Function (CTF) is selected such that it blocks high-frequency harmonics and in case of incoherent light imaging the optical system's Modulation Transfer Function (MTF) is selected such that it blocks high-frequency harmonics. The high-frequency harmonics of the object scene are thus not transferred to the imaging sensor. It should be understood, that the removal of high-frequency spatial harmonics leads to loss of information as is seen as blurring, however, this is typically preferred over aliasing.
Therefore, and as it has been noted above, the typical diffraction-limited imaging system is so tuned that even its smallest diffractive-limited spot exceeds or equals the geometrical resolution. This is to take into account that the diffractive-limited spot of a diffraction-limited system may vary in size: spots corresponding to different zoom levels of the optical system and different positions of the point source in the in-focus plane may or may not be the same. In many cases, the diffractive-limited spot is the smallest for the point source being on the optical axis and for the optical system providing the least zoom. While the latter is due to the broadening of the spot with zoom and can be seen from (B1), the former is due to the broadening of the spot at the edges of the lens and takes place due to aberrations.
In other words, the typical diffraction-limited imaging system is so tuned that it stays diffraction-limited for any position of a point source, as soon as the point source stays in the in-focus object plane, and for any level of the zoom. In this regard, it should be understood that not only the size of the diffraction-limited spot may vary depending on the location of the point source, but also the PSF itself (as a whole) may vary depending on this location. The diffraction-limited spot is merely a width of the PSF; when the shape of the PSF changes, the diffraction-limited spot also changes. Accordingly, the CTF and the MTF, respectively defined as Fourier transforms of the PSF and the squared PSF, may have one shape for one point source location and/or zoom level and another shape for another point source location and/or zoom level.
Though, in some imaging systems various elements are matched so as to create more or less the same blurring for various in-focus locations of the point source, i.e. for various lateral positions of the point source in the FOV at the in-focus plane or planes. The pixel pitch of the optical sensor, i.e. a distance from the center of one pixel to the center of an adjacent pixel, is selected to be as small as it is needed to avoid aliasing even at the least zoom. Further decrease of the pixel pitch may not improve the image quality; moreover, it may require more complex read-out circuitry, more complex further processing, and a smaller pixel size, which would cause more shot noise.
It should be noted, that though the aliasing generally presents a problem, there are techniques that can reduce its effect. An example of such a technique is the use of an optical birefringent filter. This is disclosed for example in U.S. Pat. No. 4,575,193
Moreover, there is a class of imaging techniques that utilize the aliasing for achieving the geometrical superresolution. Typically, these techniques are aimed at achieving superresolution for the whole image.
Generally, superresolution (SR) techniques are techniques aimed at achieving a spatial resolution better than its limiting resolution (i.e. the limiting resolution is not totally limiting). This limiting resolution is a larger of the diffraction-limited resolution of the optical system and the geometrical resolution of the optical sensor. Accordingly, the superresolution techniques are distributed between two main types: techniques aimed at improving imaging resolution beyond the diffraction limit, i.e. the optical superresolution techniques, and techniques aimed at improving the imaging resolution beyond the geometrical limit, i.e. the geometrical superresolution techniques.
Typical geometrical superresolution techniques use repetitive imaging of scene, for generating a sequence of slightly different geometrically-resolved images. One or more superresolved images are reconstructed from the sequence. Due to a small shift/rotation or more complex motion between the different sequential images, they contain slightly different information about the scene. The shift or motion is typically sub-pixel and needs to be “registered”. In order to improve the resolution n times along one direction, these methods typically need n images, and in order to increase the resolution n times along two directions, these methods need n2 images. In these methods, it is assumed that the scene does not change during the imaging (scan). Therefore, the system temporal resolution is sacrificed in favor of the enhanced spatial resolution. There are techniques for improving resolution of video sequence utilizing development of object in the scene.
In this connection, it is noted that, as a rule, superresolution methods sacrifice one or more of the systems' degrees of freedom in order to improve other degrees of freedom (such as spatial resolution). This is described in the publication of Z. Zalevsky, D. Mendelovic, A. W. Lohmann “Understanding superresolution in Wigner space”, J. Opt. Soc. Am., Vol. 17, No. 12, pp. 2422-2430, 2000, coauthored by the inventor of the present application.
The field of view presents another degree of freedom that can be sacrificed for obtaining the geometrical superresolution. This is described in the publication of J. Solomon, Z. Zalevsky and D. Mendlovich “Geometric superresolution by code division multiplexing”, J. Appl. Optics, Vol. 44, No. 1, pp. 32-40, January, 2005, coauthored by the inventor of the present application.
In the PCT publication WO 2004/102958, assigned to the assignee of the present application, there is presented a method and system for imaging with a geometrical superresolution for at least a part of the pixel array. There, the incoming light can be aperture coded. The aperture code can be predetermined in accordance with aliasing occurring in the imaging sensor (detector) plane and selected such as to provide orthogonality of spectral data indicative of a sampled output of the imaging sensor. The aperture code thereby enables reconstruction of an image with resolution, in at least a part of the image, enhanced by a certain factor beyond the geometrical resolution.